Skip to main content
SpringerLink
Log in

Sensitivity analysis for variational inequalities

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Sensitivity analysis results for variational inequalities are presented which give conditions for existence and equations for calculating the derivatives of solution variables with respect to perturbation parameters. The perturbations are of both the variational inequality function and the feasible region. Results for the special case of nonlinear complementarity are also presented. A numerical example demonstrates the results for variational inequalities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dafermos, S. C.,An Iterative Scheme for Variational Inequalities, Mathematical Programming, Vol. 26, pp. 40–47, 1983.

    Google Scholar 

  2. Pang, J., andChan, D.,Iterative Methods for Variational and Complementarity Problems, Mathematical Programming, Vol. 24, pp. 284–313, 1982.

    Google Scholar 

  3. Nagurney, A. B.,Stability, Sensitivity Analysis, and Computation of Competitive Network Equilibria, Brown University, PhD Dissertation, 1983.

  4. Irwin, C. L., andYang, C. W.,Iteration and Sensitivity for a Spatial Equilibrium Problem with Linear Supply and Demand Functions, Operations Research, Vol. 30, pp. 319–335, 1982.

    Google Scholar 

  5. Chao, G. S., andFriesz, T. L.,Spatial Price Equilibrium Sensitivity Analysis, Transportation Research, Vol. 18B, pp. 423–440, 1984.

    Google Scholar 

  6. Rockaffllar, R. T.,Lagrange Multipliers and Variational Inequalities, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, Wiley, New York, New York, 1980.

    Google Scholar 

  7. Mancino, O., andStampacchia, G.,Convex Programming and Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 9, pp. 3–23, 1972.

    Google Scholar 

  8. Fiacco, A. V., andMcCormick, G. P.,Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Wiley, New York, New York, 1968.

    Google Scholar 

  9. Fiacco, A. V.,Sensitivity Analysis for Nonlinear Programming Using Penalty Methods, Mathematical Programming, Vol. 10, pp. 287–311, 1976.

    Google Scholar 

  10. Fiacco, A. V.,Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York, New York, 1983.

    Google Scholar 

Download references

Author information

Author notes

  1. R. L. Tobin (Environmental Systems Engineer)

    Present address: GTE Laboratories Inc., Waltham, Massachusetts

Authors and Affiliations

  1. Environmental Research Division, Argonne National Laboratory, Argonne, Illinois

    R. L. Tobin (Environmental Systems Engineer)

Authors
  1. R. L. Tobin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. V. Fiacco

The author is indebted to A. V. Fiacco for many valuable suggestions and comments. This work was supported in part by funding from the Economic Regulatory Administration, US Department of Energy, under Contract No. W31109ENG38.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tobin, R.L. Sensitivity analysis for variational inequalities. J Optim Theory Appl 48, 191–204 (1986). https://doi.org/10.1007/BF00938597

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00938597

Key Words

Search

Navigation